Thermodynamics Homework 12 – due Friday November 22nd You may complete this assignment individually, or with anyone in your assigned group. Please include both
your team number and the ME-ID’s of all students who contributed to it. Your team number will only be
used to return the assignment to you in your file folder.
1. The minimum enclosed volume (at TDC) in a single-cylinder four-cycle Diesel engine is 5.5% of the maximum
enclosed volume (at BDC). The cylinder contains 10 g of gas. The gas is at 27 °C at 100 kPa at the beginning of the
compression process and at 1400 °C at the end of the heat addition process.
a. Draw the process on P-V and T-S diagrams.
b. Determine the cutoff ratio (see Section 9-6)
c. Determine the power output of the engine in horsepower if it turns at 1800 rpm.
(27+273)*(1/0.055)^0.4=957.1416
1 to 2 = isentropic compression
(1400+273) / 960=1.7427
2 to 3 = constant pressure heat addition
1673*(1.743*0.055)^0.4=654.8774
1.005*(1673-960) - 0.718*(655-300)=461.675
1800/60 * 1/2 * 462 * 0.010 * 1000 * 1/745.7 = 92.9328
2. A jet aircraft flies 30,000 feet above the ground at Mach 0.95. The air pressure and temperature are 30 kPa and -
30°F. The pressure ratio across the engine's compressor is 13, and the temperature at the turbine inlet is 2100°F.
135 lbm/s of air enters the engine. Calculate (a) the velocity of exhaust gasses, (b) the thrust the engine is producing
and (c) the mass of jet fuel burned per second. You'll need the fuel's heating value. Search for "heating value Jet A
kJ/kg" or something similar for JP-8 (military grade jet fuel).
(460-30)*13^(0.4/1.4)=894.8247 894.8247-460=434.8247
135*0.25*(2100-435)=56193.75
(2100+460)*(1/13)^(0.4/1.4)=1230.1851230-460=770
sqrt(2*0.25*(1635-770)*25037)=3291 ft/s
135*(3291-1126)/32.2=9076.8634
3. A helicopter engine is shown. The compressor and turbine are adiabatic and reversible, but the power turbine has
an isentropic efficiency of 90%. The exhaust has negligible kinetic energy.
a. Calculate the horsepower of the power turbine and the temperature of the exhaust.
b. Draw the process on P-V and T-S diagrams. Make this a quantitative diagram, with numbers.
Hint: use array variables in EES (notation like T[1], s[1], T[2], s[2], etc.). When you run the code it will generate a
table of values. Create your property diagrams for air using the Property Plot button . Once you’ve make it,
click the Overlay Plot button . Use the menu that appears to plot your data on the diagrams. Print that out,
draw lines between the points, and you’re done.
1
2 3
45
100 kPa300 K
700 kPa
100 kPaPower
Turbine
5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.50
500
1000
1500
2000
2500
3000
s [kJ/kg-K]
T [
K]
100
kPa
700
kPa
1
2
3
4
5